Student Name

DO N

OT

PLAC

E ST

UDE

NT

ID L

ABEL

HER

E Student Tutorial

High School

Test BookletMathematics

194985-001 ISD107541 2 3 4 5 A B C D E Printed in the USA

2

Mathematics

Unit 1

Directions:

Today, you will be taking Unit 1 of the High School Student Tutorial. The followingtasks are provided as an opportunity for you to practice with the different kinds ofquestions and response types that will be included in the PARCC Assessments.These items are from the practice tests and sample sets posted athttp://parcc.pearson.com/.

Throughout the tutorials you will see hints in boxes at the top of the item pages,to help you answer questions and understand the directions. These hints are not inthe actual test, but available only in the tutorials. The directions below will be usedduring the actual test. During the tutorial, please make sure you understand thedirections, and ask your teacher if you have any questions.

Read each question carefully. Some items will ask you to choose one correctanswer, while others will ask you to choose one or more answers. Mark youranswers by filling in the circles in your test booklet.

Do not make any stray marks in the test booklet. If you need to change an answerin your test booklet, be sure to erase your first answer completely.

Calculator Directions:

In the first section of this unit, you may not use a calculator. You will not beallowed to return to the non-calculator section of the test after you have startedthe calculator section of the test.

If you do not know the answer to a question, skip it and go on. If you finish thenon-calculator section of Unit 1 early, you may review your answers and anyquestions you may have skipped in the non-calculator section ONLY.

Do NOT go on to the calculator section in Unit 1 until directed to do so.

3

Mathematics

Using multiple-choice and multiple-select items:

Multiple-choice items have four answer choices and allow a single answer choiceto be selected.

Multiple-select items have five to eight answer choices and allow for one or moreanswer choices to be selected.

Mark your answers by filling in the circles in your Test Booklet for the answeryou choose.

4

Mathematics

Practice filling in the circles in your test booklet.

Directions for Completing the Answer Grids

1. Work the item and find an answer.

2. Write your answer in the boxes at the top of the grid.

• Print only one digit or symbol in each box. You may not need all the boxesto enter an answer, but do not leave a blank box in the middle of ananswer.

3. Under each box in which you wrote your answer, fill in the bubble that matches the number or symbol you wrote above.

• Fill in one and ONLY one bubble for each box. Do not fill in a bubble underan unused box.

• Fill in each bubble by making a solid mark that completely fills the circle.

• Fractions cannot be entered into an answer grid and will not be scored.Enter fractions as decimals.

4. See below for examples on how to correctly complete an answer grid.

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To enter –3, fill in the answer gridas follows

To enter .75, fill in the answer gridas follows

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. 7 5

5

Mathematics

Unit 1 - Section 1 (Non-Calculator)

The directions below will be used during the actual test. For the tutorial, pleasemake sure you understand the directions, and ask your teacher if you have anyquestions. At the end of each section, go back and review any items you did notanswer in that section.

This unit has two sections: a non-calculator and a calculator section.

You will now take the first section of this unit in which you may not use acalculator. You will not be allowed to return to the non-calculator section of theunit after you have started the calculator section. You will need to finish bothsections within the allotted testing time.

Once you finish the non-calculator section, read the directions in yourTest Booklet on how to continue.

6

Mathematics

M41919P_3

1. The cost to manufacture x pairs of sunglasses can be represented by afunction . If it costs $398 to manufacture 4 pairs of sunglasses, which ofthe following is true?

Select the correct equation.

C x( )

A

B

C

D

C( )4 99 50= .

C( )398 4=

C( )4 398=

C( )99 50 1. =

HINT: Multiple-choice items have four answer choices with onecorrect answer. Completely fill in the bubble in front of the correctanswer choice. Only one bubble should be filled.

7

Mathematics

VF943123_3

2. Which is a graph of the solution set of the inequality ?3 4 24x y− ≤

A B

C D

x

y

2468

-8

-6

-4

-2-8 -6 -4 -2 8642

x

y

2468

-8

-6

-4

-2-8 -6 -4 -2 642 8

x

y

2468

-8

-6-4

-2-8 -6 -4 -2 8642

x

y

24

-8

-6-4

-2-8 -6 -4 -2 8642

68

8

Mathematics

M41083P_1,2,5

3. Several points are plotted on the graph.

Which of the plotted points on the graph represent the zeros of the function Select all that apply.

y

6 8-8 -6

-8

-6

8

6

-4 -2 2 4

-4

-2

4

0

2

xE BAD

F

C

G

f x x x x( ) ( )( )?= + − −2 2 8 6

A

B

C

D

E

F

G

( , )2 0

( , )6 0

( , )0 8−

( , )−4 0

( , )−6 0

( , )0 2

( , )0 8

HINT: Multiple-select items will have five to eight answer options.

Fill in the response circles with one or more answer choices. Youmust fill in the correct number of circles for the item to beconsidered complete.

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Mathematics

VH100720_4:3,4,5

Use the information provided to answer Part A and Part B for question 4.

Consider the equation .

4. Part A

Let . Which equation is equivalent to interms of u?

( )x x2 2 23 21 10 30+ + = +

u x= +2 3 ( )x x2 2 23 21 10 30+ + = +

A

B

C

D

A

B

C

D

E

F

G

u u2 10 51 0+ + =

u u2 10 51 0− + =

u u2 10 21 0+ + =

u u2 10 21 0− + =

−4

−3

−2

0

2

3

4

Part B

What are the solutions of the equation ?

Select all that apply.

( )x x2 2 23 21 10 30+ + = +

STOP10

Mathematics

VH045903_-3

5. The figure shows the graphs of the functions The fourindicated points all have integer coordinates.

If , what is the value of

Enter your answer in the box.

y f x y g x= =( ) and ( ).

1-1-2-3-4-5-6-7-8-9 20 3 4 5 6 7 8 9

987654321

-1-2-3-4-5-6-7-8-9

x

y

y = g(x)y = f(x)

g x k f x( ) ( )= i k?

HINT: For gridded response items, your answer must be writtenand bubbled in the answer grid. To fill in a negative integer, fill inthe circle with the negative sign in the first column of the answergrid. If a negative sign is not needed, do not fill in the bubble.Fraction bars cannot be entered into answer grids. Enter fractionsas decimals. Please refer to page 4 of this tutorial, if necessary.

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You have come to the end of the non-calculator section in Unit 1 of the test.

• If you have time, review your answers in the non-calculator sectionONLY. You will not be allowed to return to the non-calculator sectiononce you have received your calculator.

• Then, raise your hand to receive your calculator before going on tothe calculator section.

STOP

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Mathematics

STOP

HINT: During the actual test, you will see a stop sign at the end ofeach section. When you reach the stop sign, review the directionsbelow it, and if there is time, review your answers from thissection only. For the tutorial, ask your teacher if you have anyquestions about the directions below. You may go on to the nextsection.

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Mathematics

Once you have received your calculator, continue with the calculator section.

Unit 1 - Section 2 (Calculator)

The directions below will be used during the actual test. For the tutorial, pleasemake sure you understand the directions, and ask your teacher if you have anyquestions. At the end of each section, go back and review any items you did notanswer in that section only.

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Mathematics

VH119723_4,8

A

B

C

D

E

F

G

H

−15

−10

−6

−4

4

6

10

15

6. The expression can be factored into the form , where a, b, and c are constants, to reveal the zeros of the

function defined by the expression. What are the zeros of the function definedby ?

Select all that apply.

3 33 1802x x− −

a x b x c( )( )+ +

3 33 1802x x− −

HINT: This is a multiple-select item with eight answer choiceslabeled A through H.

On multiple-select items the directions indicate multiple responsesare required by the word ‘all’ in the last statement, “Select all thatapply.” Fill in the response circles on your test booklet with one ormore answer choice.

14

HINT: For gridded response items, your answer must be writtenand bubbled in the answer grid. Read the directions carefully.

When completing an answer grid, do not leave empty spacesbetween integers. Fill in the circles from left to right, as necessary.

VF649975_3

7.

When the solutions to each of the two equations shown are graphed in thexy-coordinate plane, the graphs of the solutions intersect at a point. What isthe y-coordinate of the point of intersection?

Enter your answer in the box.

y x x= − −2 2 5

y x x x= − − −3 22 5 9

Mathematics

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Mathematics

VH095821_51600:1:53290:3

Use the information provided to answer Part A through Part D for question 8.

The population of a city in 2005 was 36,000. By 2010, the city’s population hadgrown to 43,800 people.

8. Part A

Assuming that the population of the city has grown linearly since 2005 andcontinues to grow at the same rate, what will be the population in 2015?

Enter your answer in the box.

Part B

Which expression is an appropriate exponential model for the population ofthe city? Let t represent the time, in years, since 2005.

A

B

C

D

36 000 1 04, .( )t

36 000 1 04 5, .( ) t

36 000 1 217, .( )t

36 000 1 217 5, .( ) t

HINT: This item has four parts. In your test booklet, there will bedesignated answer spaces that correspond with each part of theitem. Parts A and C are answer grids, while parts B and D aremultiple-choice.

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Mathematics

Part C

Assuming that the population of the city has grown exponentially since 2005and continues to grow at the same rate, what will be the population in 2015?Give your answer to the nearest whole number.

Enter your answer in the box.

A

B

C

D

1

3

5

7

Part D

Another town’s population could be modeled by the function

, where P represents the population and t represents

the time, in years, since 2005. Based on the model, by approximately what

percent does the population of this town increase each year?

P tt

( ) ( )= 27 400 1 66 10, .

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Mathematics

HINT: This is an open-response item. This item type requires youto show your reasoning and modeling in solving the item. Althoughyou may have scratch paper, only the work shown in the box in thetest booklet will be scored. Include all work andjustifications/explanations as required by the item to fully supportyour answer. Be sure to show your work and explain your answerwith clear and concise language.

VH002628

9. A chemistry student is creating mixtures of diluted acid. Beaker 1 and Beaker 2 are completely filled with mixtures and Beaker 3 is empty. Thestudent will pour the contents of Beaker 1 and Beaker 2 into Beaker 3. Thetable shows the volume of each beaker and the percent of acid containedin the mixtures for Beakers 1 and 2.

Volume (ounces)6010120

Percent of Acid20%45%

Beaker123

18

Mathematics

After the contents of Beakers 1 and 2 have been poured into Beaker 3, athird mixture will be poured into Beaker 3 to fill it completely. What is thepercent acid needed for the third mixture so that the resulting mixture inBeaker 3 will contain 30% acid?

Show your work and explain your answer.

Enter your answer and your explanation in the space provided.

19

Mathematics

HINT: This is a graphing item. You will use the coordinate plane inyour test booklet to respond to the item. Be sure to draw the lineclearly in your test booklet.

VH005322

Use the information provided to answer Part A through Part C for question 10.

The owner of a new movie theater collected attendance data for five of the sevendays of the first week the theater was open.

Tickets Sold350

275

288

1,634

1,511

Day of the WeekMonday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday

20

Mathematics

10. Part A

Provide an estimate for the total attendance for the first week. Justify thereasoning behind your estimate.

Enter your answer and your justification in the space provided.

21

Mathematics

Part B

Based on past data, new theater ticket sales after the first week arepredicted to increase by 800 tickets every 4 weeks, for 3 months(approximately 13 weeks). Using your estimate from Part A, graph a linethat can be used to predict the number of tickets sold as a function of thenumber of weeks the theater has been open.

7,200

6,400

5,600

4,8004,4004,000

0

7,600

6,800

6,000

9,200

8,400

9,600

8,800

8,000

5,200

Number of Weeks20 4 6 8 101 3 5 7 9 11 1312

x

yN

um

ber

of

Tic

kets

So

ld

22

Mathematics

Part C

Explain how you can use your graph to predict the number of tickets that willbe sold in the 13th week after the theater opened.

Enter your explanation in the space provided.

STOP

You have come to the end of the calculator section in Unit 1 of the test.

• Review your answers in the calculator section of Unit 1 only. • Then, close your test booklet and raise your hand to turn in your test

materials.

STOP

23 STOP

Mathematics

HINT: During the actual test, you will see a stop sign at the end ofeach section. When you reach the stop sign, review the directionsbelow it, and if there is time, review your answers from thissection only. For the tutorial, ask your teacher if you have anyquestions about the directions below.